Gov. Rick Scott of Florida, a Republican candidate for Senate, at his election night party on Tuesday. His race against Senator Bill Nelson, the Democratic incumbent, appears headed for a recount.CreditCreditJoe Skipper/Reuters

TALLAHASSEE, Fla. — Looming recounts in top Florida election contests, including the bitterly fought races for Senate and governor, erupted late Thursday into a fiery feud as Gov. Rick Scott, the Republican nominee for Senate who claimed victory on Tuesday, sued local elections officials in two of the state’s largest counties and accused them of “rampant fraud.”

Standing on the steps of the Governor’s Mansion, Mr. Scott announced on Thursday night that his Senate campaign had sued the Democratic elections supervisors of Broward and Palm Beach Counties. He then asked the Florida Department of Law Enforcement, which he helps oversee as governor, to investigate them.

“The people of Florida deserve fairness and transparency, and the supervisors are failing to give it to us,” Mr. Scott said. “Every Floridian should be concerned there may be rampant fraud happening in Palm Beach and Broward Counties.”

“We’ve all seen the incompetence and irregularities in vote tabulations in Broward and Palm Beach for years,” he added, “but here we go again. I will not sit idly by while unethical liberals try to steal this election from the great people of Florida.”

The lawsuits escalated tensions in the nasty and historically close political fight that has engulfed the leaders of the nation’s largest presidential battleground state in the 48 hours since the polls closed on Tuesday. The turmoil threatens to stretch out over weeks as recounts take place and, inevitably, more legal challenges wind up in court.

Mr. Scott celebrated his apparent win on Tuesday against Senator Bill Nelson, the Democratic incumbent. But the vote gap between them has only narrowed since, as the state’s largest counties have continued to tally ballots that were mailed in or cast on a provisional basis on Election Day.

Mr. Scott questioned why Broward County in particular continued to increase its vote totals over two days, suggesting the origin of the ballots being tallied was suspicious. The local elections supervisor has said mail-in and provisional ballots were being counted as quickly as possible.

The gap has also closed in the governor’s race, which is now in recount territory as well. Andrew Gillum, a Democrat, conceded to Ron DeSantis, a Republican, late Tuesday night, shortly before The Associated Press called the race for Mr. DeSantis. But Mr. DeSantis’s victory margin has since shrunk to 0.44 percentage points — six-hundredths of a point below the recount threshold. Mr. DeSantis leads by more than 36,000 votes.

Florida’s 67 counties have until noon on Saturday to submit their unofficial vote totals to the state’s Division of Elections. Four more contests — for state agriculture commissioner, one State Senate seat and two State House seats — are also likely to be headed for recounts. The lead in the agriculture commissioner race flipped on Thursday afternoon: Nikki Fried, a Democrat, moved ahead of Matt Caldwell, a Republican, by 2,884 votes.

The highest-profile recount possibility so far, however, is in the United States Senate race. As of Thursday night, 15,127 votes separated Mr. Scott and Mr. Nelson, a difference of 0.18 percentage points. Under Florida law, a margin smaller than 0.5 points prompts a machine recount, and a margin of 0.25 points or less requires a more thorough manual recount.

“From where I sit, it is a virtual certainty,” said Marc Elias, Mr. Nelson’s elections lawyer and a veteran of prominent recounts around the country. “I think that it is fair to say right now that the results of the 2018 Senate election are unknown.”

Mr. Elias went even further, predicting that outstanding ballots would ultimately put Mr. Nelson over the top, though that possibility continued to seem unlikely.

Image

Supporters of Mr. Nelson on Election Day. Under Florida law, a vote margin of half a percentage point prompts a recount.CreditJeff J Mitchell/Getty Images

“At the end of this process, we believe Senator Nelson is going to be declared the winner,” Mr. Elias said.

Mr. Scott’s campaign and the National Republican Senatorial Committee, according to court records, asked for emergency hearings to force Brenda C. Snipes, the elections supervisor of Broward County, to publicly release vote totals, and to require Susan Bucher, the elections supervisor of Palm Beach County, to allow campaign representatives to witness the review of potentially defective ballots.

Dr. Snipes, who like Ms. Bucher is an elected official, had told reporters on Thursday afternoon that she could not say how many votes were left to count.

“I think we had over 58 percent of our voters voted, and each voter received a ballot package of either five or six pages,” she said when asked about why counting was taking so long. “It’s volume that causes this.”

Her performance is of particular concern to Republicans because a court ruled in May that her office had illegally destroyed some ballots from a 2016 congressional race. As a result, the office has been under state monitoring. Broward and Palm Beach, the state’s second- and third-largest counties, both lean heavily Democratic and have a history of slow ballot counting. Miami-Dade, the state’s largest county, counted faster than Broward and Palm Beach, in part because its officials worked through the night after Election Day.

“The goal here is to see that all the votes in Florida are counted and counted accurately,” Dan McLaughlin, a campaign spokesman, said in a statement. “Rick Scott’s action appears to be politically motivated and borne out of desperation.”

Results from Broward so far indicate that nearly 25,000 people cast votes for governor but not for senator, even though the Senate race came first on the ballot.

Enthusiasm for Mr. Gillum’s candidacy may account for some of the difference, since he excited many voters who cared chiefly about electing him. But some Democrats believe that the design of the Broward ballot used in the county played a role: The Senate contest appeared in the bottom left-hand corner of the first page, beneath the instructions to voters, where it may have been easily overlooked.

Mr. Elias said the difference between the votes for senator and governor in the county was significant, but he refrained from criticizing the ballot layout, at least for now.

Once counties report their unofficial totals to the state on Saturday, Secretary of State Ken Detzner, an appointee of Mr. Scott, will be able to order any of the legally mandated recounts.

A statewide machine recount would have to be completed by 3 p.m. on Nov. 15, Mr. Elias said. If that process yields a margin of less than 0.25 percentage points in any federal or state races, then Mr. Detzner would order manual recounts in those races of what are known as undervotes and overvotes; the recounts would have to be completed by Nov. 18.

In the Senate race, undervotes are ballots on which optical-scanning machines detected a vote for another race down the ballot, like governor or attorney general, but no selection for Senate. Overvotes are ballots on which scanners detected that the voter had marked more than one choice in the race.

Florida voters fill in paper ballots by hand using a pen, and no longer cast the punch-card ballots that produced the infamous “hanging chads” in the 2000 presidential election.

Candidates cannot request recounts, but those with fewer votes in a race can refuse them.